Abstract: The use of supplementary information on auxiliary variables in sample surveys was extensively discussed by Cochran and Jessen. In their work they showed that regression estimator is superior to the other estimators (viz. ratio and mean per unit estimators etc.).This paper proposes a new kind of estimator based on appropriate weighing of the sample means of the main and the auxiliary variables. It is shown that the proposed estimator is more efficient when compared with the regression, ratio and the mean per unit estimator under certain restrictions on the correlation coefficient between main and the auxiliary variables.